It is 100 years since the well-known Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory �yield criteria, failure criterion, etc � of materials �including metallic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc� under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a brief discussion of the computational implementation of the strength theories and multi-axial fatigue. �DOI: 10.1115/1.1472455�

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Current design practice of concrete-filled steel tube (CFST) columns uses different formulas for different section profiles to predict the axial load bearing capacity. It has always been a challenge and practically important issue for researchers and design engineers who want to find a unified formula that can be used in the design of the columns with various sections, including solid, hollow, circular and polygonal sections. This has been driven by modern design requirements for continuous optimization of structures in terms of not only the use of materials, but also the topology of structural components. This paper extends the authors' previous work [1] on a unified formulation of the axial load bearing capacity for circular hollow and solid CFST columns to, now, including hollow and solid CFST columns with regular polygonal sections. This is done by taking a circular section as a special case of a polygonal one. Finally, a unified formula is proposed for calculating the axial load bearing capacity of solid and hollow CFST columns with either circular or polygonal sections. In addition, laboratory tests on hollow circular and square CFST long columns are reported. These results are useful addition to the very limited open literature on testing these columns, and are also as a part of the validation process of the proposed analytical formulas. Keywords：Concrete-filled steel tube (CFST), hollow and solid section, circular and polygonal section, load bearing capacity Notations sc f combined strength of CFST sc ϕ stability factor of CFST 0

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